Equation 677 Database

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Magma 2bb18881d33c…

magma 2bb18881d33c
Size
399
Isomorphism class hash
2bb18881d33ca36618f480d8012b6c1d4604834d5bff1de95f776367ddd88619
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 18:28:22
Display reorder
238,239,240,241,242,234,235,236,237,247,248,249,250,251,243,244,245,246,380,327,307,253,38,328,39,308,254,329,40,309,255,310,330,41,256,331,42,311,257,332,43,312,258,324,44,313,259,325,36,314,260,326,37,306,252,47,336,316,262,48,337,317,263,49,338,318,264,50,339,319,265,51,340,320,266,52,341,321,267,53,333,322,268,45,334,323,269,46,335,315,261,391,385,386,392,295,114,194,18,296,19,115,195,288,20,116,196,108,289,21,197,290,22,109,189,291,23,110,190,292,24,111,191,293,25,112,192,294,26,113,193,27,304,123,187,28,305,124,188,29,297,125,180,30,298,117,181,31,299,118,182,32,300,119,183,33,301,120,184,34,302,121,185,35,303,122,186,383,389,390,384,71,6,128,210,63,211,7,129,64,212,8,130,1,65,213,131,66,214,0,132,67,215,2,133,68,207,3,134,69,208,4,126,70,209,5,127,203,55,15,137,204,56,16,138,205,57,17,139,206,58,9,140,198,59,10,141,199,60,11,142,200,61,12,143,201,62,13,135,202,54,14,136,388,398,397,387,348,280,342,176,350,177,281,344,352,178,282,346,283,354,179,349,356,171,284,351,358,172,285,353,343,173,286,355,345,174,287,357,347,175,279,359,169,367,273,360,170,368,274,362,162,370,275,364,163,372,276,366,164,374,277,369,165,376,278,371,166,361,270,373,167,363,271,375,168,365,272,377,394,395,396,393,95,219,150,87,96,88,220,151,97,89,221,152,222,98,81,144,90,82,223,145,91,83,224,146,92,84,216,147,93,85,217,148,94,86,218,149,80,104,228,159,72,105,229,160,73,106,230,161,74,107,231,153,75,99,232,154,76,100,233,155,77,101,225,156,78,102,226,157,79,103,227,158,379,381,378,382 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#398832895e3bd2abf5e43b28ae50fd39c13e336f20eb0dffe5fd92657a9cb3b8, M = the submagma generated by {0} (19 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 21.

last edited by qawbecrdtey at 2026-10-08 18:28:23 · history